Midpoint

The midpoint of the segment (x₁, y₁) to (x₂, y₂)

The midpoint (also known as class mark in relation to histogram) is the middle point of a line segment. It is equidistant from both endpoints.

Formulas

The formula for determining the midpoint of a segment in the plane, with endpoints (x₁) and (x₂) is:

$\frac{x_1 + x_2}{2}$

The formula for determining the midpoint of a segment in the plane, with endpoints (x₁, y₁) and (x₂, y₂) is:

$\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$

The formula for determining the midpoint of a segment in the space, with endpoints (x₁, y₁, z₁) and (x₂, y₂ z₂) is:

$\left(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2}, \frac{z_1 + z_2}{2}\right)$

More generally, for an n-dimensional space with axes $x_1, x_2, x_3, \dots, x_n\,\!$, the midpoint of an interval is given by:

$\left(\frac{x_{1_1} + x_{1_2}}{2}, \frac{x_{2_1} + x_{2_2}}{2}, \frac{x_{3_1} + x_{3_2}}{2}, \dots , \frac{x_{n_1} + x_{n_2}}{2} \right)$

Construction

The midpoint of a line segment can be located by first constructing a lens using circular arcs, then connecting the cusps of the lens. The point where the cusp-connecting line intersects the segment is then the midpoint. It is more challenging to locate the midpoint using only a compass, but it is still possible.^[1]

See also

• Midpoint polygon
• Median (geometry)
• Segment bisector
• Numerical integration

References

1. ^ "Wolfram mathworld". 29 September 2010. http://mathworld.wolfram.com/Midpoint.html. 

External links

• Animation - showing the characteristics of the midpoint of a line segment

This geometry-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Elementary geometry Geometry stubs Wikimedia Foundation. 2010. Игры ⚽ Нужно решить контрольную? Zone diet 1745 in science Look at other dictionaries: midpoint — UK US /ˈmɪdpɔɪnt/ noun [C, usually singular] ► a point in the middle of a period of time: »We are about to reach the midpoint of the summer season …   Financial and business terms midpoint — index center (central position), norm Burton s Legal Thesaurus. William C. Burton. 2006 …   Law dictionary midpoint — (n.) late 14c., from MID (Cf. mid) + POINT (Cf. point) (n.) …   Etymology dictionary midpoint — [mid′point΄] n. a point at or close to the middle or center, or equally distant from the ends …   English World dictionary midpoint — [[t]mɪ̱dpɔɪnt[/t]] also mid point 1) N SING: oft N between/of n The midpoint between two things is the point that is the same distance from both things. ...the midpoint between Paris and Warsaw. ...the midpoint of the front of your house. 2) N… …   English dictionary midpoint — n. 1) to reach a midpoint 2) at (the) midpoint * * * [ mɪdpɔɪnt] at (the) midpoint to reach a midpoint …   Combinatory dictionary midpoint — /mid poynt /, n. 1. a point at or near the middle of, or equidistant from, both ends, as of a line: the midpoint of a boundary. 2. a point in time halfway between the beginning and the end, as of a process, event, or situation: the midpoint of… …   Universalium midpoint — mid|point [ˈmıdpɔınt] n [C usually singular] a point that is half of the way through or along something midpoint of ▪ At the midpoint of the study, all those taking part were interviewed again …   Dictionary of contemporary English midpoint — mid|point [ mıd,pɔınt ] noun singular or uncount 1. ) a place that is HALFWAY between two other places 2. ) the time that is HALFWAY through a process or activity: the midpoint of something: By the midpoint of the fight, we knew who would win …   Usage of the words and phrases in modern English midpoint — UK [ˈmɪdˌpɔɪnt] / US noun [singular/uncountable] 1) the time that is halfway through a process or activity the midpoint of something: By the midpoint of the fight, we knew who would win. 2) a place that is halfway between two other places …   English dictionary 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”